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Cost of the Trip

Math brain teasers require computations to solve.


Puzzle ID:#728
Fun:** (2.09)
Difficulty:** (1.71)
Submitted By:vikass***




Michelle rents a car to take her to the airport in the morning and return her home that evening. Halfway to the airport, she picks up a friend who accompanies her to the airport. That night, she and her friend return back to Michelle`s place. The total cost is $20.00. If the amount is to be split fairly, how much money should Michelle pay?

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Jun 28, 2004

an explanation would be nice.
Jul 14, 2004

Explanation: -----
The correct answer depends on what is considered "fair". -----
1) vikass must have thought this way: -----
Each half-trip from or to the airport costs $5. Michelle has to pay the first half-trip alone, plus half of the other three half-trips. $5 + $2.50 + $2.50 + $2.50 = $12.50. -----
2) But would this be more fair: -----
the return trip should be split evenly, $5 each. -----
on the trip to the airport, Michelle went the whole distance, the friend half of that; so Michelle should pay twice as much as her friend for those $10, i.e. Michelle $6.67 and the friend $3.33 (fractions of a cent cannot be paid). This way Michelle would pay $11.67 in all. -----
3) Or again, look at it this way: Michelle went 4 half-distances, the friend 3; so Michelle ought to pay 4/7 of the $20, i.e. $11.43. -------
4 etc.) but that is not all, read on...
Jul 14, 2004

More explanation: -----

4) So far we have only considered the $20 for the car rental (to simplify let's assume that includes fuel and insurance). But did the friend share the driving? Probably not, and almost certainly not in the exact proportion considered fair in one of the 3 options treated in the previous comment. ----- How much would it be fair for the friend to give Michelle for the driving and for having made the rental arrangements? $5, $10, or whatever a taxi would have charged (penhaps $30)? -----

5) On the other hand, what kind of a friend is that which makes her friend pay for a ride? If Michelle is a real friend, should'nt she pay the whole $20 without ever mentioning money to her friend?
Aug 02, 2004

I think the brain teaser's answer is wrong!

If michelle rents a car and travells to the airport and back, picking up a friend who lives half way to the airport who also travels back to ichelle's house then michelle travels a distance of 4x and her friend travels a distance of 3x. This gives a total of 7x of travel.

The cost of the journey is $20 therefore each x is worth $20/7, therefore michelle's portion of the journey must be worth $20/7 X 4. $11.43 (approx).
Mar 04, 2006

I agree with the last choice. Michelle was going anyway, and ought to be thankful for the company of her friend.
Apr 23, 2006

For this teaser, we need to add a mirkiness factor to those of fun and difficulty. Has anyone noticed that the friend did not get on a plane? So the friend either guards the car and should ride free, or the friend drives the rental all day and should pay most of the cost.
May 23, 2006

There are 7 half distances, but (for the sake of the teaser) you have to assume that there are really 8, and Michelle counted as 2 in the first half distance.
May 23, 2006

Sorry for the double comment, but I just realized something. The whole trip cost $20, making one 'half distance' cost $5, no matter how many people there are in the car. That means Michelle pays the whole $5 for the first 'half distance' and $2.50 each for the last three, adding up to $12.50! Good teaser, BTW!
Feb 05, 2007

thats a cheap rent-a-car
Jan 28, 2009

I had $11.43 (4/7).

Poorly worded teaser, but this solution seems like the "fairest".
Mar 28, 2009

With no other constraints the answer would appear to be $11.43

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